Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#16810462 |
| Fitting | C2×C32×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×SD64 |
112 conjugacy classes of subgroups.
1702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27304670, C4×#16810462, #27304682, … |
| maximal normal subgroup of | #27304670, C4×#16810462, #27304682, … |
| maximal quotient of | C2×#20272894, C2×#20272897, C2×#20272917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6812);